1. Field of the Invention
This invention is applicable to any digital communications receiver utilizing digital time domain timing recovery in conjunction with digital equalization. It can be used with bandlimited RZ-rate sampled RZ signals, twice oversampled NRZ signals, and arbitrary signals with low-pass or bandpass channel impairment.
2. Description of Related Art
Fundamental to the operation of a digital communications receiver is the conversion of its incoming received waveform from continuous time to representative samples at discrete time instances. It is well-known in the art that if the sampling rate is sufficiently high relative to the finite bandwidth of the received waveform, it and the discrete time sample sequence (henceforth referred to as the “digital signal”) can be considered equivalent, in the sense that one can be reconstructed from the other by a series of well-defined mathematical operations. On the other hand, it is often desirable for receiver power efficiency and complexity to sample at or below the minimum rate permissible for reconstruction of the received waveform from its discrete time sample sequence. In such cases, the performance of the digital receiver (as measured by the error rate in recovering the transmitted data) can be strongly dependent on the sampling time instances, i.e., there exist relatively good, such as optimal, choices for the sampling instances. These relatively good sampling instances may not be a fixed pattern in time, i.e., periodic, depending upon the type of distortion the data-bearing waveform undergoes after transmission through the channel to the receiver. For example, the transmitted waveform can suffer from time-varying delay as well as fixed delay and phase distortion as it is transmitted over the channel to the receiver. This time-varying delay manifests itself as jitter while the time-varying phase results in frequency offset, both of which can be highly detrimental to the performance of the receiver. “Timing recovery” refers to the process of instantaneously adjusting the received waveform sampling instances for better or relatively good receiver performance. In a digital communications receiver, this timing adjustment can occur at various points within the signal processing path, e.g., at an analog-to-digital converter (ADC) or at a delay line.
In cases where the transmitter has embedded timing information, e.g., timing beacons or pilots, into the transmitted waveform, timing recovery can be relatively straightforward if the timing information can be reliably extracted and processed at the receiver. Such an approach, however, typically incurs overhead in terms of the data transmission rate, so communications systems often use data-bearing waveforms without explicitly embedded timing information. For these cases, the receiver recovers the correct timing from the received waveforms without prior knowledge of the transmitted data. The subject matter of this disclosure pertains to this class of timing recovery techniques.
The problem of timing recovery is exacerbated in the presence of standard linear impairments such as frequency-dependent amplitude and phase variation, i.e., the channel response. It is well-known in the art that it is significantly advantageous to perform timing recovery on the received waveform after these standard linear impairments are compensated, e.g., by a linear equalizer. Otherwise, the time-domain intersymbol interference manifested between consecutive data pulses in the received waveform (due to the channel response) results in low performance for many timing recovery techniques. When the channel response to be equalized is not known a priori or is time-varying, adaptive equalizers are often employed to compensate the channel response. In the context of digital communications systems with sampled waveforms, such an adaptive equalizer comprises a number of coefficients which it adaptively adjusts repeatedly to reduce or minimize some error criteria, e.g., the mean-square error between the equalizer output samples and the corresponding decoded data symbols. Linear impairments can be adequately compensated by linear equalizers which can be divided into two main classes: infinite and finite impulse response (IIR and FIR equalizers, respectively). Both classes of equalizers are capable of adaptively compensating the standard linear impairments of a channel and, as such, can be considered candidates for adaptive equalization of the received digital signal prior to timing recovery. Unfortunately, operating a linear adaptive equalizer simultaneously in series with a timing recovery apparatus can be relatively difficult due to the interaction between the group delay characteristic of the equalizer and the subsequent timing adjustment computed by the timing recovery apparatus.
In recognition of the problems posed by operating a timing recovery apparatus on the equalized output of a linear adaptive equalizer, works in the current state of the art typically attempt to coordinate the adaptation of the equalizer with the timing adjustment imparted by the timing recovery apparatus. One technique is to either adapt the equalizer or adjust the timing by the timing recovery apparatus but not simultaneously. A straightforward generalization of this technique is to ensure that the timing adjustment process of the timing recovery apparatus operates and adjusts timing much faster than the group delay characteristic of the equalizer updates. Another general class of techniques attempts to constrain the equalizer adaptation or coefficients in some fashion to fix its group delay characteristic. For all these techniques, empirical evidence is offered to demonstrate their efficacy but the ultimate ability of proposed techniques to prevent the interaction between the timing correction of the linear equalizer and that from the timing recovery apparatus is not or cannot be proven by design. Indeed, those skilled in the art will acknowledge that, even with these techniques, the group delay characteristic of the linear adaptive equalizer and the timing adjustment of the timing recovery apparatus can both drift imperceptibly slowly in opposite directions such that the serial combination of the equalizer and timing recovery apparatus appears to have a fixed delay. Given sufficient time for the linear equalizer and timing recovery apparatus to adapt and operate, however, it has been observed that these opposing timing drifts can lead to a condition in which both may realize excessive time delays which compromise overall system performance. A specific example is the case where the linear equalizer is a FIR filter with a limited number of coefficients. As the timing adjustment of the timing recovery apparatus drifts in one direction, the FIR filter compensates by inducing a proportionately opposite drift which uses a similar shift or delay in its coefficients. For example, a one sample delay in the FIR filter (with other frequency characteristics held constant) is realized approximately by shifting a zero coefficient to become the filter's first coefficient, the first coefficient to become the second one, the second coefficient to becomes the third one, etc (a one sample advance is similar). It is straightforward to see that if this timing drift continues unabated, the equalizer loses progressively its ability to compensate the channel response as its filter coefficients are truncated successively to zero. On the other hand, the timing recovery apparatus outputs a timing adjustment whose magnitude is ever increasing, to the point that the timing adjustment range of the ADC, e.g., is exceeded. Clearly, this operational condition would be undesirable. One improvement on the state of the art for embodiments disclosed herein is an immunity to this timing interaction between the linear adaptive equalizer and the timing recovery apparatus. This immunity is fundamental in the sense that it is assured from first principles as opposed to merely by simulation evidence.
The following publications are representative of the current state of the art for timing recovery methods operating with adaptive equalizers: (1) Coker, R. et al. Implementation of PRML in a Rigid Disk Drive, IEEE Transactions on Magnetics, Vol. 27, No. 6, November 1991, pgs 4538-4543; (2) Gysel, P. and Gilg, D. Timing Recovery in High Bit-Rate Transmission Systems Over Copper Pairs, IEEE Transactions on Communications, Vol. 46, No. 12, December 1998, pgs 1583-1586; (3) U.S. Pat. No. 5,818,655; (4) U.S. Pat. No. 5,999,355; and (5) U.S. Pat. No. 6,804,695.
These works propose various techniques to either decouple or constrain the adaptation of the coefficients of the equalizer with respect to the timing adjustments imparted by the timing recovery apparatus. A representative example of the former class of techniques is described in Gysel and Gilg, where the timing recovery entity is allowed to modify the input timing of the linear adaptive equalizer only when the latter is not adapting, i.e., is frozen. Similarly, the equalizer adapts only when its input timing as determined by the timing recovery entity is held constant. While the technique is described using a single iteration between the timing adjustment from the timing recovery entity and the adaptation of the equalizer, those skilled in the art will recognize that even repeated cycling between the two operational modes can result in inherently suboptimal overall timing adjustment (comprising the serial combination of the timing adjustment from the timing recovery entity and the group delay response of the adapted equalizer) compared to one in which both the equalizer and the timing recovery entity are allowed to modify (simultaneously) their respective parameters.
In the second class of techniques, Coker et al. propose a method to constrain the adaptive equalizer be a three coefficient FIR filter with a fixed “centre” coefficient and symmetric “side” (real) coefficients, i.e., h is of the form h=[a, b, a]T. With these constraints, the resultant equalizer response is guaranteed (by design) to have linear phase and uniform (zero) group delay over the sampling frequency range. Unfortunately, the effective limitation to two adaptive coefficients and rigid flat group delay response constraint render the equalizer insufficiently flexible in many applications to provide adequate performance, although the timing interaction with any timing recovery entity is inherently minimized by this design. The apparatus described in U.S. Pat. No. 5,818,655 extends this method to the general multicoefficient case where the FIR filter equalizer adaptation is constrained to produce only symmetric coefficients, resulting in a flat equalizer group delay response and the same advantages/disadvantages with respect to equalization performance vs. timing stability. Recognizing that requiring a flat equalizer group delay over the entire sampling bandwidth can overly constrain the gain and phase equalization performance of the adaptive equalizer, U.S. Pat. No. 5,999,355 proposes a method to “anchor”, i.e., fix, the equalizer gain and phase response at a single frequency (the extension to multiple gain and phase constraints at multiple frequencies is readily apparent to those skilled in the art). For example, this single anchor frequency can be chosen intuitively to coincide with the spectral peak of the expected equalizer input signal. The motivation behind this technique is clear, in that it is expected that the equalizer can perform better when it is afforded greater flexibility to shape its phase/group delay response around the anchor frequency. Nonetheless, those skilled in the art will recognize that a single (or even multiple) frequency constraint(s) on the adaptive equalizer gain or phase response does not, by design, guarantee that the corresponding group delay response will not interact with the recovered timing signal from the timing recovery entity as previously described. Indeed, it is simple to construct realistic examples of signals and channels (such as a low-pass cable model) for which the adaptive equalizer will modify slowly its group delay response around the anchor frequency in such a way as to induce a steady drift in the timing recovery signal from the timing recovery entity. Thus, the technique described in U.S. Pat. No. 5,999,355 does not adequately address the fundamental problem of timing interaction between a timing recovery entity and a linear adaptive equalizer when the former modifies the input timing of the latter as a result of examining the latter's output.